标题： 基于学习理论的先验用于贝叶斯推断：早期暗能量的一个案例研究 显示英文标题

标题： Learning Theory Informed Priors for Bayesian Inference: A Case Study with Early Dark Energy

摘要： 宇宙学模型通常用粒子物理的语言来提出和表述，使用如轴子衰变常数等量，但通过假设对后者的均匀先验来使用看似物理的量（如能量密度比）进行数据测试。 这种方法忽略了来自基本理论（包括粒子物理和弦理论）对模型的先验，例如对亚普朗克轴子衰变常数的偏好。 我们引入了一种新颖的方法，利用归一化流（NF），一种灵活的生成式机器学习技术，在无法获得或难以计算解析表达式时生成模型参数的先验。 作为测试案例，我们关注早期暗能量（EDE）模型，该模型旨在解决哈勃张力问题。 而不是对$\textit{phenomenological}$EDE 参数$f_{\rm EDE}$和$z_c$使用均匀先验，我们根据轴子质量与衰变常数的理论预期对EDE宇宙学进行训练。 我们的方法在这一表示中恢复了已知的约束，同时在总CPU计算时间方面效率提高了$\sim 300,000$倍。 Applying our NF to $\textit{Planck}$ and BOSS data, we obtain the first theory-informed constraints on EDE, finding $f_{\rm EDE} \lesssim 0.02$ at $95\%$ confidence with an $H_0$ consistent with $\textit{Planck}$, but in $\sim 6\sigma$ tension with SH0ES. This yields the strongest constraints on EDE to date, additionally challenging its role in resolving the Hubble tension. 显示英文摘要

摘要： Cosmological models are often motivated and formulated in the language of particle physics, using quantities such as the axion decay constant, but tested against data using ostensibly physical quantities, such as energy density ratios, assuming uniform priors on the latter. This approach neglects priors on the model from fundamental theory, including from particle physics and string theory, such as the preference for sub-Planckian axion decay constants. We introduce a novel approach to learning theory-informed priors for Bayesian inference using normalizing flows (NF), a flexible generative machine learning technique that generates priors on model parameters when analytic expressions are unavailable or difficult to compute. As a test case, we focus on early dark energy (EDE), a model designed to address the Hubble tension. Rather than using uniform priors on the $\textit{phenomenological}$ EDE parameters $f_{\rm EDE}$ and $z_c$, we train a NF on EDE cosmologies informed by theory expectations for axion masses and decay constants. Our method recovers known constraints in this representation while being $\sim 300,000$ times more efficient in terms of total CPU compute time. Applying our NF to $\textit{Planck}$ and BOSS data, we obtain the first theory-informed constraints on EDE, finding $f_{\rm EDE} \lesssim 0.02$ at $95\%$ confidence with an $H_0$ consistent with $\textit{Planck}$, but in $\sim 6\sigma$ tension with SH0ES. This yields the strongest constraints on EDE to date, additionally challenging its role in resolving the Hubble tension.